## Additional Notes on Probability September 10, 2009

Posted by Ms. Miller in Algebra I.

I felt we rushed through this, so here are a couple of things I wanted to add:

Combinations

• OR – when you see this word, you should ADD the individual probabilities.
• AND – when you see this word, you should MULTIPLY the individual probabilities.
• NOT – when you see this word, you can either ADD all the other probabilities or you can take the probability of the event’s happening and SUBTRACT that from 1. Example: The probability of NOT rolling a 2 on a die is $1-\frac{1}{6}=\frac{5}{6}$.

Whenever you are combining two or more events together, you have to be aware of whether you are resetting the circumstances of the trial if that is possible. For example, if you have two spinners, one with numbers and one with colors, you don’t have to worry about replacing or resetting anything. On the M&M trials we did, however, we really should have talked about replacement. For example: If you had 30 M&Ms, of which 6 were red and 4 were green, and I asked you the theoretical probability of drawing a red M&M and then drawing a green M&M, you would multiply the probabilities (because of the AND), but the number in the denominator would change because you would no longer have 30 M&Ms when you made the second draw: $\frac{6}{30} * \frac{4}{29}=\frac{24}{870}=\frac{1}{145}$

A standard deck has 52 cards divided into 4 different sets, called “suits”: hearts and diamonds, which are red, and spades and clubs, which are black. Each suit has 13 cards numbered from 1 (ace) to 10, and the the face cards Jack, Queen, and King. So, for example, the probability of drawing a red card would be $\frac{2\ \mathrm{suits}}{4\ \mathrm{suits}}=\frac{1}{2}$. The probability of drawing a 7 would be $\frac{4\ \mathrm{7s}}{52\ \mathrm{cards}}=\frac{1}{13}$.